Question

# Consider the population of four juvenile condors. Their weights in pounds are : 2, 3, 6,...

Consider the population of four juvenile condors. Their weights in pounds are : 2, 3, 6, 10 (a) Let x be the weight of a juvenile condor. Write the possible unique values for x: (NOTE: Separate each value in the list with a comma.) ANS = 2,3,6,10 (b) Find the mean of the population: ANS = 5.25 (c) Let x¯ be the average weight from a sample of two juvenile condors. List all possible outcomes for x¯. (If a value occurs twice, make sure to list it twice.) This is the sampling distribution for samples of size 2: (NOTE: Separate each value in the list with a comma.) ? (d) Find the mean of the sampling distribution: ?

c)

Sample Average weight
(2,2) 2
(2,3) 2.5
(2,6) 4
(2,10) 6
(3,2) 2.5
(3,3) 3
(3,6) 4.5
(3,10) 6.5
(6,2) 4
(6,3) 4.5
(6,6) 6
(6,10) 8
(10,2) 6
(10,3) 6.5
(10,6) 8
(10,10) 10

The sampling distribution for samples of size 2: 2, 2,5, 2,5, 3, 4, 4, 4.5, 4.5, 6, 6, 6, 6.5, 6.5, 8, 8, 10

d)

Sample mean Probability
2 1/16 = 0.0625
2.5 2/16 = 0.125
3 1/16 = 0.0625
4 2/16 = 0.125
4.5 2/16 = 0.125
6 3/16 = 0.1875
6.5 2/16 = 0.125
8 2/16 = 0.125
10 1/16 = 0.0625

mean of the sampling distribution = 2 * 1/16 + 2.5 * 2/16 + 3 * 1/16 + 4 * 2/16 + 4.5 * 2/16 + 6 * 3/16 + 6.5 * 2/16 + 8 * 2/16 + 10 * 1/16 = 5.25

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